Ultrafast 2D IR spectroscopy of the excess proton in liquid water

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Science  02 Oct 2015:
Vol. 350, Issue 6256, pp. 78-82
DOI: 10.1126/science.aab3908

How well does water share its protons?

Chemists have spent centuries trying to understand what acids look like at the molecular level. It's clear now that water molecules in the liquid accommodate extra protons. Less clear is whether the protons piggyback on individual water molecules (Eigen structure) or find shared accommodation between two at a time (Zundel structure). Thämer et al. acquired time-resolved vibrational spectra across an unusually broad span of the mid-infrared, allowing them to monitor stretches and bends at the same time. Their results imply a more prominent role for the Zundel structure than previously anticipated.

Science, this issue p. 78


Despite decades of study, the structures adopted to accommodate an excess proton in water and the mechanism by which they interconvert remain elusive. We used ultrafast two-dimensional infrared (2D IR) spectroscopy to investigate protons in aqueous hydrochloric acid solutions. By exciting O–H stretching vibrations and detecting the spectral response throughout the mid-IR region, we observed the interaction between the stretching and bending vibrations characteristic of the flanking waters of the Zundel complex, [H(H2O)2]+, at 3200 and 1760 cm−1, respectively. From time-dependent shifts of the stretch-bend cross peak, we determined a lower limit on the lifetime of this complex of 480 femtoseconds. These results suggest a key role for the Zundel complex in aqueous proton transfer.

Acid-base chemistry and most biological redox chemistry are governed by the transport of protons through water. Aqueous proton transfer is generally accepted to occur along hydrogen bonds through sequential hops of an excess proton from one solvating water molecule to the next. Although this widely accepted picture, known as the Grotthuss mechanism, captures the concept of long-range charge translocation without transport of a particular proton, numerous basic questions remain regarding the rapidly evolving structure of an aqueous proton (1). Does the dominant structure resemble the Eigen complex, H3O(H2O)3+ (a triply hydrated hydronium ion), or the Zundel complex, H(H2O)2+ (a proton that is equally shared between two water molecules)? What are the relative stabilities of these species? How do they interconvert during proton transport, and what role does the dynamics of solvating water molecules play in this process? Though these questions have been studied extensively via molecular dynamics (MD) simulations (14), experiments that entail visualizing time-dependent proton structures on femtosecond time scales have not been carried out. To address such questions, we performed ultrafast infrared (IR) spectroscopy experiments to observe the time-dependent vibrations associated with an excess proton within the fluctuating potential defined by its solvating water. Our experiments on hydrochloric acid solutions offer evidence for the presence of a metastable Zundel complex with a sufficiently long lifetime that it cannot only be a transition state between Eigen configurations.

A number of computational studies employing ab initio MD and empirical valence bond simulations have been performed to investigate the nature of the solvated proton. These studies have reached varying conclusions regarding the dominant structure of the solvated proton (Zundel or Eigen) and the proton-transport mechanism (2, 512). Several mechanisms have been described that involve the exchange of Zundel and/or Eigen complexes with varying degrees of distortion or delocalization. In part, these differing interpretations reflect the difficulty in classifying Zundel and Eigen species within a continuum of rapidly evolving hydrogen bond configurations. The variations of hydrogen bond lengths and angles between the two structures are small, and thermal fluctuations cause them to undergo rapid distortions (2). To gain insight into these processes and to help answer the questions presented above, experiments that can identify Zundel and Eigen configurations in the liquid phase and directly monitor the time evolution of these structures are required.

Aqueous proton configurations and their ultrafast interconversion give rise to broad overlapping spectral features in the linear IR absorption spectrum of strong acids. In addition to the O–H stretch absorption (3400 cm−1) and the HOH bend vibration (1650 cm−1) that arise from bulk-like water, the IR spectra of strong acids feature a broad absorption continuum that extends from the O–H stretching band to frequencies below 1000 cm−1 (Fig. 1) (13). This was originally explained by noting that the functional form of the potential of a proton shared by two oxygens could vary strongly between weakly anharmonic (for a proton bound to one of the water molecules) and double well (an equally shared proton) and that the vibrational transitions associated with these potentials would span the entire continuum band (14). The continuum is not entirely featureless, however, but shows a “shoulder” on the high-frequency side of the H2O bend (1760 cm−1) and a broad absorption maximum at 1200 cm−1 (15).

Fig. 1 Infrared spectra for water (blue trace) and 4 M HCl (red trace).

The black solid trace indicates the difference spectrum between 4 M HCl and water. The dashed trace represents the spectrum of the pump pulses used in the nonlinear experiments. Cartoons represent the proposed vibrational assignments of the different spectral features to vibrations of the solvated proton. The vibrations of the excess proton, bulk water, and flanking water molecules are shaded green, blue, and red, respectively. The horizontal dashed line is the zero line for the difference spectrum.

Although a detailed experimental assignment correlating IR continuum frequencies to Eigen and Zundel structures in the liquid phase is missing, one may turn to gas-phase studies of protonated water clusters (1618), MD simulations (1922), and ab initio calculations (23) for guidance. Gas-phase studies offer the ability to determine the vibrational spectra of well-defined Zundel and Eigen structures. Though it is unclear whether assignments of specific structures and vibrational modes from gas-phase studies will carry into the liquid phase, they provide insight into the correlated vibrational frequency shifts between different proton configurations. Based on the consistent observations across these studies, we propose the assignments shown in Fig. 1. Cluster studies (17, 20, 21) measure the O–H stretching vibrations of the Eigen species’ hydronium core at 2650 cm−1, and MD simulations indicate that its breadth in the liquid spans several hundred wave numbers (19, 22). As one hydrogen bond of the three-coordinate Eigen complex is strengthened, a “special pair” is formed (10), shifting the structure toward the Zundel configuration. Consequently, the hydronium O‒H stretching frequency of that hydrogen bond is red-shifted, whereas the frequency of the other two is blue-shifted. In the limiting case of a Zundel complex, the vibrational frequency of the shared proton is deeply red-shifted into the frequency range of the broad peak at 1200 cm−1, whereas the flanking water molecules have a stretching frequency near 3200 cm−1 (17, 21, 22). Meanwhile, the feature at 1760 cm−1 has been associated with the bending vibration of the flanking waters of the Zundel complex (1618, 22, 23). Given the strong anharmonicity of the system, these assignments are meant only as a simplified representation of more complex vibrations of mixed character. Even so, these assignments indicate that beneath the broad overlapping features there are characteristic frequencies associated with different structural motifs of the solvated proton (19, 21, 22).

With these assignments in mind, we performed ultrafast two-dimensional IR (2D IR) spectroscopy on 1 to 5 M hydrochloric acid solutions to spectroscopically characterize the protonated water species and their associated dynamics. In these experiments, O–H stretching vibrations were excited with a pair of 45-fs pulses that have a center frequency of 3150 cm−1 and a bandwidth of 400 cm−1 (Fig. 1, dashed trace). The center frequency was tuned to the red side of the O–H stretching band to preferentially excite strongly hydrogen-bonded water species that participate in proton hydration. The response to this excitation was subsequently probed with a sub–70-fs broadband pulse with a spectrum ranging from 1500 to 4000 cm−1. 2D IR experiments measure the change in absorption at the detection frequency ω3 after excitation at a frequency ω1 and waiting a period of time τ2. The broad spectral bandwidth of the probe pulse makes it possible to study couplings between O–H stretch vibrations and different vibrational modes throughout the mid-IR region. Cross peaks in a 2D IR spectrum reveal correlations between features in the linear IR spectrum and provide a stringent test of vibrational assignments. From this analysis, we can identify the presence of different solvation structures of the excess proton and follow their evolution on the femtosecond time scale.

The 2D IR spectra of 4 M HCl for several waiting times τ2 are shown in Fig. 2. Comparison of the 2D IR spectra of HCl and H2O for τ2 = 100 fs reveals three common features that have been described previously for H2O (24): (i) the bleach of the O–H stretch along the diagonal axis at ω3 = 3200 cm−1 (red), (ii) an elongated induced absorption that tails from ω3 = 3100 to <1500 cm−1 (blue), and (iii) a cross peak between the O–H stretch and bend vibrations at (ω1, ω3) = (3300, 1650 cm−1). A notable difference between the spectra of pure water and the acid solutions is the diagonally elongated line shape of the O–H stretch peak for 4 M HCl. This feature is attributable to inhomogeneous broadening and reflects the strong hydrogen bonding interactions between the excess proton and water.

Fig. 2 Two-dimensional IR spectra of 4 M HCl in H2O as a function of waiting time τ2.

Bleaches are in red, induced absorptions in blue. The τ2 = 100 fs spectrum of H2O is shown for comparison. Center lines are depicted in white on the O–H stretch bleach. Detection frequencies corresponding to the Zundel bend and H2O bend are labeled δZ and δW, respectively.

Of particular interest is a previously unobserved stretch-bend cross peak that appears at ω3 = 1760 cm−1. This peak becomes more apparent in concentration-dependent 2D IR spectra when the smoothly varying background between ω3 = 2000 and 1500 cm−1 is subtracted (Fig. 3C). A projection onto ω3 indicates that this peak corresponds to the Zundel bend transition observed in the linear IR spectrum (Fig. 3, B and D) and that it increases linearly with acid concentration (Fig. 3A).

Fig. 3 Concentration dependence of 2D IR experiments.

(A) Amplitude of the Zundel stretch-bend cross peak as a function of proton concentration with linear fit. a.u., arbitrary units. (B) FTIR spectra of 4 M HCl (red) and water (blue) in the bending region identifying the bulk water bend (δW) and Zundel bend (δZ) frequencies. (C) 2D IR spectra for water, 2 M HCl, and 4 M HCl at τ2 = 100 fs after subtraction of the background contribution. (D) Projection of 2D IR spectra (by integrating the spectra between ω1 = 2900 and 3500 cm−1). Spectra for water (blue curve, top), 2 M HCl (yellow curve, middle), and 4 M HCl (red curve, bottom) are shown with corresponding fits from the spectral decomposition (black dotted lines). The blue and red dotted lines indicate the contribution of the δZ and δW components, respectively. Green dotted lines show the background.

Qualitatively, the dominant changes to the 2D IR spectra that occur with increasing waiting time can be divided into the rapid relaxation of the initial transient spectral features and the growth of a “long-time” spectrum that persists over the time scale of thermal diffusion. The desired structural and dynamical information of the liquid is encoded in the decaying spectral components, which have relaxation times between 80 and 765 fs, depending on both ω1 and ω3. The long-time spectrum, which grows on a 675-fs time scale, is characterized by spectral changes in the detection dimension ω3 that are similar to a linear difference spectrum due to a rise in temperature (see supplementary materials). This “hot ground state” (HGS) spectrum has been attributed to rapid nonadiabatic vibrational energy relaxation into strongly coupled low-frequency intermolecular modes, which shifts vibrational resonances in the same manner as a temperature increase (2426). No obvious correlation between amplitude growth and waiting time was observed in the spectral region attributed to the O–H stretch vibrations of hydronium or the Eigen complex (2000 to 2800 cm−1).

Additionally, the rapid loss of inhomogeneous broadening can be quantified by the decay of the center line slope (CLS) (27). The CLS decay time depends strongly on acid concentration, growing from 100 fs in neat water to 240 fs in 4 M HCl (see supplementary materials). Thus, irreversible vibrational relaxation of the initial O–H stretch excitation is substantially faster than the loss of initial O–H frequency memory. Because O–H frequency shifts require intermolecular structural changes, this is a clear indication of vibrationally nonadiabatic relaxation (24).

To further analyze the stretch-bend cross peaks, we isolated the contributions of interest by performing a linear spectral decomposition of the stretch-bend cross-peak region (ω3 < 1900 cm−1). Four distinct, physically meaningful components were needed to reconstruct the entirety of the data: (i) a stretch-bend cross peak at the frequency of the bulk water bend vibration, (ii) a stretch-bend cross peak arising from solvated protons, (iii) an HGS spectrum, and (iv) a sloping background. The procedure is explained in detail in the supplementary materials. Figure 3D illustrates the decomposition at τ2 = 100 fs for different proton concentrations.

The results of the 2D IR spectral decomposition at τ2 = 50 and 600 fs are shown in Fig. 4A. The decomposition reveals the correlation between stretch and bend frequencies associated with the excess proton in water and separates this component from the overlapping stretch-bend cross peak of bulk H2O. At the earliest waiting time, the peaks are clearly separated in excitation and detection frequency, with the proton stretch-bend cross peak at (ω1, ω3) = (3185, 1760 cm−1) and the bulk H2O stretch-bend cross peak at (ω1, ω3) = (3260, 1650 cm−1).

Fig. 4 Shape and time evolution of the stretch-bend cross peaks after decomposition.

(A) Presentation of the three dominant components for 2D IR spectra of 4 M HCl for waiting times of τ2 = 50 and 600 fs. Grid lines illustrate the Zundel (red) and water (blue) peak frequencies. (B) Projections of the stretch-bend cross peaks onto one frequency axis: ω1 for stretch (ν) and ω3 for bend (δ). These bleach signals are inverted to present a positive spectrum. (C) Evolution of the peak frequency of the Zundel stretch-bend cross peak in ω1 with increasing waiting time. The blue dotted line indicates the asymptotic value.

The proton stretch-bend cross peak characterizes two coupled vibrational modes of the aqueous proton. Although the assignments of the features in the IR spectrum of HCl in Fig. 1 have varying degrees of uncertainty, the measurement of two correlated vibrational modes of the same molecular species provides considerably higher constraints. A projection of this cross peak onto the ω1 and ω3 axes presented on a common frequency axis (Fig. 4B) provides an indication of the stretch and bend line shapes, as well as their overlap with the corresponding water vibrations. The observed frequencies for the proton correspond closely to the predicted stretching and bending vibrations of the Zundel complex (17, 22), providing evidence for the vibrational assignments and the presence of this complex. We use the term “Zundel” in a broad sense, to refer to a pair of vibrationally coupled water molecules flanking a shared proton. Additional computational investigations are needed to relate the vibrational frequencies to simulation parameters such as the proton-sharing parameter δ that characterizes the difference in distances between the excess proton and its two nearest oxygen atoms, as well as todifferentiate symmetric Zundel configurations from strongly bound asymmetric special-pair configurations.

The presence of the Zundel complex in liquid water raises the question of its population among the protonated water complexes. In principle, our vibrational assignments indicate that we can spectrally separate the Zundel complex from bulk water in the bend region of the linear IR spectrum. The ratio of their peak amplitudes can then be used to determine a concentration if we know the ratio of the corresponding transition dipole moments (TDMs). In practice, this exercise is fraught with complications, such as how delocalization of the Zundel complex influences its apparent concentration and TDM, and uncertainty about the frequency of the Eigen bend. However, within certain approximations, such an estimate is still informative. The amplitude ratio of Zundel bend to H2O bend FTIR absorption peaks is ~2:5 in 4 M HCl. If we generously estimate the bend TDM for the Zundel species at a factor of 10 larger than that of the bulk water bend (28), the FTIR peak amplitudes result in a Zundel species concentration of 1.6 M, or 40% of the solvated protons. Because a more conservative estimate of the TDM would result in a larger Zundel concentration, we view 40% as the minimum fraction. This implies that the Zundel complex makes up a substantial, if not dominant, fraction of the protonated species in HCl solutions.

As illustrated by the grid lines marking the peak positions at τ2 = 50 and 600 fs (Fig. 4A), the Zundel stretch-bend cross peak blue-shifts along the excitation axis with increasing waiting time, asymptotically approaching the bulk water stretch excitation frequency. The shift reflects the growing probability of initially exciting the O–H stretch vibration of bulk water and detecting this excitation in the bending of a Zundel complex after waiting for a time τ2. A fit to the Zundel peak frequency in ω1 as a function of τ2 reveals that this shift occurs on a time scale of 480 fs (Fig. 4C).

The spectral shifting could originate from either proton transport or vibrational excitation transfer. In the former case, the initially excited H2O accepts a proton, becoming a Zundel complex, whereas in the latter, only vibrational energy is transferred between the two species as a result of strong vibrational coupling between bulk water and the Zundel bend. Because both processes can contribute, the 480-fs time scale sets a lower bound for the exchange time between bulk water molecules and the Zundel complex. Vibrational energy transport and relaxation are important contributors to our data. Figure S6 in the supplementary materials illustrates the time-dependent amplitudes of components from the stretch-bend cross-peak decomposition, as well as the relaxation of the O–H stretch excited-state absorption. The excited O–H stretching vibrations evolve rapidly, exchanging energy among various modes on an 80-fs time scale. The resulting dissipation into intermolecular motions gives rise to the HGS signature, which grows on a time scale of 675 fs. The stretch-bend cross peaks decay on time scales of 410 fs for the Zundel complex and 765 fs for water. As a result, the observed shifting of the Zundel stretch-bend cross peak is likely dominated by the intermolecular vibrational energy transport, raising the possibility that the Zundel persistence time is markedly longer.

To draw further conclusions regarding the proton-transfer mechanism, we must distinguish between momentary configurations resulting from fast fluctuations and structures that are long-lived relative to the hydrogen bond dynamics of water. In the former case, the excess charge may be delocalized over multiple water molecules fluctuating about a mean position but not moving, on average; in the latter case, the charge is translocated, leaving no memory of its origin (3, 6). We refer to the latter case as proton transfer. In this work, we observe the Zundel complex through spectroscopic properties imposed by the [H(H2O)2]+ core. Even if the excess charge could oscillate between more than two water molecules while the average charge position remains localized, the stretch-bend frequency correlation in the cross peak would be preserved. Therefore, the >480-fs persistence time for the Zundel configuration corresponds to long-range proton-transfer events. Earlier studies involving IR transient absorption experiments reported sub–100-fs exchange times between Eigen and Zundel species (29, 30). Questions about the role of vibrational energy transport aside, we believe that these experiments are reporting on localized proton fluctuations rather than long-range charge transport.

Because we did not observe the Eigen species in the experiments described here, we cannot draw conclusions regarding its stability or role in aqueous proton transfer. However, we note that no sign of vibrational excitation transfer was observed from the Zundel stretch into the region characteristic of Eigen configurations (2000 to 2800 cm−1). A relatively long-lived Zundel complex represents an important part of the proton-transfer mechanism; this configuration is not merely a fleeting transition state traversed during an Eigen-to-Eigen proton transfer. In addition to Zundel-to-Zundel transport, exchange processes involving Zundel-to-Eigen transport are still consistent with our data. It is less clear how a barrierless Zundel-Eigen interconversion would be observed in our experiments. Deeper insight into the mechanism can be gained from ultrafast IR spectroscopy of the Eigen complex using excitation pulses in the window between 2000 and 2800 cm−1, where the Eigen species or special-pair configurations are expected to absorb. Such experiments are planned for the future, as is investigation of the peak at 1200 cm−1 in the acid continuum. Studies at lower concentrations are also needed to definitively evaluate the role of ion pairing in aqueous proton transfer (31, 32). Although many unanswered questions remain regarding the proton-transport mechanism in water, our findings place important constraints on the role of the Zundel complex in this process.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S6

References (33, 34)

References and Notes

  1. Acknowledgments: This work was supported by the U.S. Department of Energy (grants DE-SC0011456 and DE-SC0014305). M.T. thanks the Deutscher Akademischer Austauschdienst for a postdoctoral fellowship. L.D.M. thanks the Natural Sciences and Engineering Research Council of Canada for a scholarship.
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